At first I thought hunting but now it's making me think of seagulls. Mainly because of the last two lines; there are tons of seagulls and you can run after them and they'll just walk away.

Colours I perceive beyond your sight
I sit in the trees and often take flight
With peeps and chirps and whistles too
It is not uncommon to find me in a zoo
But not just any am I that you will see around
Once I have it I will stick with the love I found